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Björnsson, Jóhann ; Giesl, Peter ; Hafstein, Sigurdur Freyr ; Kellett, Christopher M. ; Li, Huijuan:
Computation of continuous and piecewise affine Lyapunov functions by numerical approximations of the Massera construction.
Department of Mathematics, University of Bayreuth
Bayreuth
,
2014
. - 6 S.
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Angaben zu Projekten
| Projekttitel: |
Offizieller Projekttitel Projekt-ID Marie-Curie Initial Training Network "Sensitivity Analysis for Deterministic Controller Design" (SADCO) 264735-SADCO The Icelandic Research Fund, Grant 130677- 052 ARC Future Fellowship FT1101000746 Humboldt Research Fellowship Ohne Angabe |
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Abstract
The numerical construction of Lyapunov functions provides useful information on system behavior. In the Continuous and Piecewise Affine (CPA) method, linear programming is used to parameterize a CPA Lyapunov function for continuous nonlinear systems. This method is relatively slow due to the linear program that has to be solved. A recent proposal was to parameterize the CPA Lyapunov function based on a Lyapunov function in a converse Lyapunov theorem by Yoshizawa. In this paper we propose parameterizing CPA Lyapunov functions using a Lyapunov function construction in a classic converse Lyapunov theorem by Massera. We provide the theory for such a parameterization and present several examples to illustrate the utility of this approach.
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| Publikationsform: | Preprint, Postprint |
|---|---|
| Keywords: | Lyapunov methods; nonlinear control systems; asymptotic stability; linear programming; Massera construction; approximation methods; continuous systems |
| Institutionen der Universität: | Fakultäten Fakultäten > Fakultät für Mathematik, Physik und Informatik Fakultäten > Fakultät für Mathematik, Physik und Informatik > Mathematisches Institut Fakultäten > Fakultät für Mathematik, Physik und Informatik > Mathematisches Institut > Lehrstuhl Mathematik V (Angewandte Mathematik) Profilfelder Profilfelder > Advanced Fields Profilfelder > Advanced Fields > Nichtlineare Dynamik |
| Titel an der UBT entstanden: | Ja |
| Themengebiete aus DDC: | 500 Naturwissenschaften und Mathematik > 510 Mathematik |
| Eingestellt am: | 28 Mär 2015 22:00 |
| Letzte Änderung: | 30 Mär 2015 07:13 |
| URI: | https://eref.uni-bayreuth.de/id/eprint/9470 |
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